This special focus, started in the summer of 2002, follows the design of our Center's pioneering special focus on Mathematical Support for Molecular Biology. In this special focus, the center seeks to:

- Develop and strengthen collaborations and partnerships between mathematical scientists (mathematicians, computer scientists, operations researchers, statisticians) and biological scientists (biologists, epidemiologists, clinicians).
- Identify and explore issues in mathematics and computer science that need to be resolved to make progress on important problems in epidemiology.
- Identify and explore methods of mathematical science not yet widely used in studying problems of epidemiology and introduce epidemiologists to them - with an emphasis on methods of discrete mathematics (including discrete probability) and the algorithms, models, and concepts developed in the field of theoretical computer science.
- Introduce outstanding young people from both the mathematical/computer science and biological communities to the issues and problems and challenges of computational and mathematical epidemiology.
- Involve biological and mathematical scientists together to define the agenda and develop the tools of computational and mathematical epidemiology.

The special focus will consist of a research program featuring "working groups" concentrating on specific research topics and a program integrating research and education through a series of workshops and tutorials. The 1994-2000 DIMACS Special Focus on Mathematical Support for Molecular Biology played a central role in laying the groundwork for the field of computational molecular biology, led many fledgling concepts and methods grounded in the mathematical sciences to become standard tools in the biological sciences, produced lasting partnerships between biological and mathematical scientists, and introduced many of today's leaders in computational biology to the field and to each other. We are confident that this special focus will do the same.

Epidemic models of infectious diseases go back to Daniel Bernoulli's
mathematical analysis of smallpox in 1760 and have been developed
extensively since the early 1900s. Hundreds of mathematical models
have been published since, exploring the effects of bacterial,
parasitic, and viral pathogens on human populations. The results have
highlighted and formalized such concepts as the notion of a core
population in sexually transmitted diseases and made explicit other
concepts such as herd immunity for vaccination policies. Relating to
persistent infections, key pathogens that have been studied are:
Malaria, *Neisseria gonorrheae*, *M. tuberculosis*, *HIV*, and *T. palladum*.
Important issues such as drug-resistance, rate of spread of infection,
epidemic trends, and the effects of treatment and vaccination all have
been addressed through mathematical modeling approaches, which with
the help of computational tools have provided new insights. Yet, for
many infectious diseases, we are far from understanding the mechanisms
of disease dynamics. The strength of the modeling process is that it
can lend insight and clarification to existing data and theories.
Mathematical models provide a unique approach to representing and
studying the integrated behavior of complex biological systems and
enable us to compare and contrast existing theories of the dynamic
interactions in a complex system. The size of modern epidemiological
problems and the large data sets that arise call out for the use of
powerful computational methods for studying these large models. As
pointed out by Levin, Grenfell, Hastings, and Perelson in a 1997
article in *Science*, "imaginative and efficient computational
approaches are essential in dealing with the overwhelming complexity
of [such] biological systems." New computational methods are need to
deal with the dynamics of multiple interacting strains of viruses
though the construction and simulation of dynamic models, the problems
of spatial spread of disease through pattern analysis and simulation,
and the optimization of drug design through hierarchical and other
search methods on adaptive landscapes.

Statistical methods have long been used in mainstream epidemiology largely for the purpose of evaluating the role of chance and confounding associations. Considerable effort is expended by epidemiologists to ferret out sources of systematic error ("bias and confounding") in the observations and to evaluate the role of uncontrollable error (using statistical methods) in producing the results. Interpretation of the results usually depends upon correlative information from the medical and biological sciences. The role of statistical methods in epidemiology is changing due to the large data sets that are arising and this calls for new methods and new approaches, making use of modern information technology for dealing with huge data sets of information on disease patterns.

A smaller but venerable tradition within epidemiology has considered the spread of infectious disease as a dynamical system and applied difference equations and differential equations to that end. But little systematic effort has been made to apply today's powerful computational methods to these dynamical systems models and few computer scientists have been involved in the process. We hope to change this situation. Probabilistic methods, in particular stochastic processes, have also played an important role. However, here again, few computer scientists have been involved in efforts to bring the power of modern computational methods to bear.

A variety of other potentially useful approaches to epidemiological issues have not yet attracted the attention of many in the computer science community nor are the methods made widely available to biological scientists. For example, many fields of science, and in particular molecular biology, have made extensive use of the methods and techniques of discrete mathematics (broadly defined), especially those that exploit the power of modern computational tools. These are guided by the algorithmic and modeling methods of theoretical computer science that make these tools more available than they have been in the past. Yet, these methods remain largely unused in epidemiology. One major development in epidemiology that makes the tools of discrete mathematics and theoretical computer science especially relevant is the use of Geographic Information Systems (GIS). These systems allow analytic approaches to spatial information not used previously. Another development is the availability of large and disparate computerized databases on subjects containing information on many attributes that might be related to disease status.

The role of discrete mathematics and theoretical computer science has also become important with the increasing emphasis in epidemiology of an evolutionary point of view. To fully understand issues such as immune responses of hosts; co-evolution of hosts, parasites, and vectors; drug response; and antibiotic resistance; among others, biologists are increasingly taking approaches that model the impact of mutation, selection, population structure, selective breeding, and genetic drift on the evolution of infectious organisms and their various hosts. Epidemiologists are only beginning to become aware of some of the computer science tools available to analyze these complex problems, such as methods of classification and phylogenetic tree reconstruction grounded in concepts and algorithms of discrete mathematics and theoretical computer science and developed in connection with the explosion in "computational biology," a field in which DIMACS has been a pioneer. Many of the recent methods of phylogenetic tree reconstruction resulted from the DIMACS Special Focus on Mathematical Support for Molecular Biology are described in the DIMACS website in the reports on the accomplishments of the earlier Special Focus. Yet, a great deal more needs to be done.

One important modern topic in theoretical computer science that arose in epidemiology is the theory of group testing, which arose in connection with testing millions of World War II military draftees for syphilis. The idea is to avoid testing each individual and instead to divide them into groups and determine if some individual in the group is positive for the disease, updating the process with groups that test positive. The modern theory of group testing is heavily influenced by combinatorial methods, in particular by the methods of combinatorial designs and coding theory, and many modern algorithmic methods, developed by theoretical computer scientists, are not yet widely known or used in epidemiology.

Mathematical methods of formal logic and ordered algebraic systems have been used to develop the foundations for a theory of measurement with important uses in the physical sciences and, more recently, in the social and biological. While this kind of measurement theory has been applied to data analysis in the social and biological sciences, it is virtually unknown in the epidemiology community (where the term "measurement theory" has other connotations), except to the extent that epidemiological studies use principles, grounded in but sometimes challenged by measurement theory, such as that certain kinds of statistical tests are inappropriate for ordinal data.

New interdisciplinary approaches, involving partnerships among mathematical scientists and biological scientists, epidemiologists, and clinicians, offer promise for making progress on modern epidemiological problems and should take both fields of epidemiology and mathematics/computer science in new and fruitful directions. Mathematical and computational methods seem especially relevant in light of recent modeling approaches to emerging infectious diseases such as the vector-borne diseases from West Nile virus, Eastern equine encephalitis virus and Borrelia burgdorfei (Lyme disease); the spread of "mad cow" disease (transmissable spongiform encephalopathy; and HIV/AIDS. Control measures for these diseases often have counter-intuitive consequences only revealed after sophisticated mathematical analysis.

Similar advances as a result of applications of mathematical and computational modeling have not been as evident in the area of chronic disease epidemiology, although work of considerable promise is being done, for example on modeling of the progression of cancer. In this special focus, we will consider both infectious and non-infectious diseases, and we will explore mathematical and computational approaches to animal and plant diseases as well as to human diseases.

Opportunities to participate:

**Workshops:**a variety of workshops and mini-workshops are planned.

**Working Groups:**Interdisciplinary "working groups" will explore special focus research topics.

**Tutorial Program:**annual tutorials to introduce researchers/students to various topics in the field.

**Visitor Programs:**Applications for research and graduate student visits to the center are invited. Some funds are available for travel and local support.

**Postdoctoral Positions:**There is a possibility that postdoctoral positions will be offered in this area.

**Graduate Student Support:**Funds will be set aside for graduate students interested in attending workshops. Students interested in visiting DIMACS during the special focus are encouraged to apply under our visitor program.

**Publications:**We anticipate that a variety of publications, including AMS-DIMACS books, technical reports, abstracts and notes on the WWW, and DIMACS Modules will result from the special year.

Index of Special Focus on Computational and Mathematical Epidemiology

DIMACS Homepage

Contacting the Center

Document last modified on December 3, 2009.